An Eigenvalue Approach to Analyzing a Finite Source Priority Queueing Model

Steve Drekic and Winfried Grassmann

Annals of Operations Research, 2002, vol. 112, issue 1, 139-152

Abstract: In this paper, we present a novel approach to determining the steady-state distribution for the number of jobs present in a 2-class, single server preemptive priority queueing model where the low priority source population is finite. Arrivals are assumed to be Poisson with exponential service times. The system investigated is a quasi birth and death process, and the joint distribution is derived via the method of generalized eigenvalues. Using this approach, we are able to obtain all eigenvalues and corresponding eigenvectors explicitly. Furthermore, we link this method to the matrix analytic approach by obtaining an explicit solution for the rate matrix R. Two numerical examples are given to illustrate the procedure and highlight some important computational features. Copyright Kluwer Academic Publishers 2002

Keywords: priority queues; generalized eigenvalues; quasi-birth-and-death process; matrix analytic methods (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (7)

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DOI: 10.1023/A:1020933122382

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